Related papers: The common ancestor type distribution of a $\Lambd…
Consider a two-type Moran population of size $N$ with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to $N$,…
In populations competing for resources, it is natural to ask whether consuming fewer resources provides any selective advantage. To answer this question, we propose a Wright- Fisher model with two types of individuals: the inefficient…
Consider a haploid population of fixed finite size with a finite number of allele types and having Cannings exchangeable genealogy with neutral mutation. The stationary distribution of the Markov chain of allele counts in each generation is…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
Known results on the moments of the distribution generated by the two-locus Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical methods…
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the…
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of…
The Wright-Fisher model describes a biological population containing a finite number of individuals. In this work we consider a Wright-Fisher model for a randomly mating population, where selection and mutation act at an unlinked locus. The…
We consider a population evolving under mutation and selection. The genotype of an individual is a word of length $\ell$ over a finite alphabet. Mutations occur during reproduction, independently on each locus; the fitness depends on the…
We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet of…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
The transition distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of…
Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of…
We present a new model for seed banks, where direct ancestors of individuals may have lived in the near as well as the very far past. The classical Wright-Fisher model, as well as a seed bank model with bounded age distribution considered…
We consider the mutation--selection differential equation with pairwise interaction (or, equivalently, the diploid mutation--selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the…
Motivated by seminal paper of Kozlov et al.(1975) we consider in this paper a branching process with a geometric offspring distribution parametrized by random success probability $A$ and immigration equals $1$ in each generation. In…
The Wright-Fisher model is the most popular population model for describing the behaviour of evolutionary systems with a finite population size. Approximations to the model have commonly been used for the analysis of time-resolved genome…